Comparison of stochastic mortality models using Slovak data
Keywords:
Age-specific mortality rates, Lee-Carter model, CBD model, Haberman-Russolilo method, Least Squared method, ARIMAAbstract
The aim of the paper is to compare the two most well-known stochastic mortality models – Lee-Carter (LC) model and Cairns-Blake-Dowd (CBD) model, using mortality data of the Slovak population. Mortality data come from mortality.org and cover the period from the establishment of the Slovak Republic (1993) to 2017. The least squares method was used to estimate the parameters of the models, as well as the method of Haberman and Russolilo. The autoregressive integrated moving average model ARIMA was applied to predict time-dependent parameters. The mortality forecast is set for the next three years. The results were simply compared numerically and graphically showing the differences between the models that prove the existence of the modeled risk.References
1. Cairns, A. J., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Ong, A., Balevich, I.: A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal 13.1, 1-35, (2009).
2. Cairns, A. J., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Khalaf-Allah, M.: Mortality density forecasts: An analysis of six stochastic mortality models. Insurance: Mathematics and Economics 48.3, 355-367, (2011).
3. Chavan, R., Ramkrishna, S.: Modeling and Forecasting Mortality Using the Lee-Carter Model for Indian Population Based on Decade-wise Data. Sri Lankan Journal of Applied Statistics 17.1 (2016).
4. Haberman, S., Russolillo, M.: Lee Carter mortality forecasting: application to the Italian population. Actuarial Research Paper No. 167, Cass Business School, London (2005).
5. Heligman, L., Pollard, J. H.: The age pattern of mortality. Journal of the Institute of Actuaries 107.1 (1980).
6. Human Mortality Database, mortality.org
7. Jiang, L.: Changing kinship structure and its implications for old-age support in urban and rural China. Population Studies 49.1 (1995).
8. Koissi, M., Shapiro, A. F., Högnäs, G.: Evaluating and extending the Lee–Carter model for mortality forecasting: Bootstrap confidence interval. Insurance: Mathematics and Economics 38.1 (2006).
9. Lee, R. D., Carter, L. R.: Modeling and forecasting US mortality. Journal of the American statistical association 87.419 (1992).
10. Lee, R.: The Lee-Carter method for forecasting mortality, with various extensions and applications. North American actuarial journal 4.1 (2000).
11. McNown, R., Rogers A.: Forecasting mortality: A parameterized time series approach. Demography 26.4 (1989).
12. Milevsky, M. A., Promislow, S. D.: Mortality derivatives and the option to annuitise. Insurance: Mathematics and Economics 29.3 (2001).
13. Nocito, S.: Stochastic Mortality Projections: A Comparison of the Lee-Carter and the Cairns-Blake-Dowd models Using Italian Data. University of Studies of Turin (2015).
14. Pitacco, E., Denuit, M., Haberman, S., Olivieri, A.: Modelling longevity dynamics for pensions and annuity business. Oxford University Press (2009).
15. Safitri, Y. R., Mardiyati, S., Malik, M.: The Cairns-Blake-Dowd model to forecast Indonesian mortality rates. In AIP Conference Proceedings (Vol. 2168, No. 1, p. 020039). AIP Publishing LLC (2019).
16. SAS Institute Inc: "SAS/ETS® 13.2 User’s Guide – The ARIMA procedure". Cary, NC: SAS Institute Inc (2014)
17. Singh, A., Ram, F.: Forecasting mortality in India. Population, Health and Development in India: Changing Perspective, TK Roy, M. Guruswamy, and Arokiaswamy, Rawat Publication Mumbai, India (2004).
18. Šoltésová, T.: Aktuárske modelovanie v životnom poistení. 1. vydanie. Bratislava: Vydavateľstvo Letra Edu. (2019).
19. Wilmoth, J. R.: 13 Mortality Projections for Japan. Health and mortality among elderly populations (1996).
20. Yadav, A., Yadav, S., Kesarwani, K.: Decelerating mortality rates in older ages and its prospects through Lee-Carter approach. PloS one 7.12 (2012).
2. Cairns, A. J., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Khalaf-Allah, M.: Mortality density forecasts: An analysis of six stochastic mortality models. Insurance: Mathematics and Economics 48.3, 355-367, (2011).
3. Chavan, R., Ramkrishna, S.: Modeling and Forecasting Mortality Using the Lee-Carter Model for Indian Population Based on Decade-wise Data. Sri Lankan Journal of Applied Statistics 17.1 (2016).
4. Haberman, S., Russolillo, M.: Lee Carter mortality forecasting: application to the Italian population. Actuarial Research Paper No. 167, Cass Business School, London (2005).
5. Heligman, L., Pollard, J. H.: The age pattern of mortality. Journal of the Institute of Actuaries 107.1 (1980).
6. Human Mortality Database, mortality.org
7. Jiang, L.: Changing kinship structure and its implications for old-age support in urban and rural China. Population Studies 49.1 (1995).
8. Koissi, M., Shapiro, A. F., Högnäs, G.: Evaluating and extending the Lee–Carter model for mortality forecasting: Bootstrap confidence interval. Insurance: Mathematics and Economics 38.1 (2006).
9. Lee, R. D., Carter, L. R.: Modeling and forecasting US mortality. Journal of the American statistical association 87.419 (1992).
10. Lee, R.: The Lee-Carter method for forecasting mortality, with various extensions and applications. North American actuarial journal 4.1 (2000).
11. McNown, R., Rogers A.: Forecasting mortality: A parameterized time series approach. Demography 26.4 (1989).
12. Milevsky, M. A., Promislow, S. D.: Mortality derivatives and the option to annuitise. Insurance: Mathematics and Economics 29.3 (2001).
13. Nocito, S.: Stochastic Mortality Projections: A Comparison of the Lee-Carter and the Cairns-Blake-Dowd models Using Italian Data. University of Studies of Turin (2015).
14. Pitacco, E., Denuit, M., Haberman, S., Olivieri, A.: Modelling longevity dynamics for pensions and annuity business. Oxford University Press (2009).
15. Safitri, Y. R., Mardiyati, S., Malik, M.: The Cairns-Blake-Dowd model to forecast Indonesian mortality rates. In AIP Conference Proceedings (Vol. 2168, No. 1, p. 020039). AIP Publishing LLC (2019).
16. SAS Institute Inc: "SAS/ETS® 13.2 User’s Guide – The ARIMA procedure". Cary, NC: SAS Institute Inc (2014)
17. Singh, A., Ram, F.: Forecasting mortality in India. Population, Health and Development in India: Changing Perspective, TK Roy, M. Guruswamy, and Arokiaswamy, Rawat Publication Mumbai, India (2004).
18. Šoltésová, T.: Aktuárske modelovanie v životnom poistení. 1. vydanie. Bratislava: Vydavateľstvo Letra Edu. (2019).
19. Wilmoth, J. R.: 13 Mortality Projections for Japan. Health and mortality among elderly populations (1996).
20. Yadav, A., Yadav, S., Kesarwani, K.: Decelerating mortality rates in older ages and its prospects through Lee-Carter approach. PloS one 7.12 (2012).
Downloads
Published
2021-06-02
Issue
Section
Articles
